Hampshire Constabulary are appealing for witnesses following incidents during and after Pompey’s match against Oldham last Saturday.
Some supporters entered the field of play, while there were reports of disorder outside the stadium following the final whistle.
Officers would like to identify the people involved in these incidents so they can speak to them as part of their enquiries.
Superintendent Ali Heydari said: “We are working in partnership with Portsmouth Football Club to investigate reports of aggressive behaviour at Saturday’s match, and are keen to obtain any information to establish the exact circumstances and the identities of those involved.
“There were a large number of spectators at the match who will no doubt have seen the incidents inside and outside the stadium, and we believe that people may have captured what happened on camera or on their mobile phones.
“We are appealing for anyone who has any still or moving footage of these incidents, or any information to help us identify the people involved, to come forward and speak to us.
“Further to this, if you know who was involved, or you yourself were involved, then please call us on 101 so we can continue to assess the nature of what happened.
“Our officers work closely with Portsmouth Football Club and violent or aggressive behaviour will not be tolerated. Not only could you face a criminal penalty, but you may face further sanctions from the club.”
Chief Executive Mark Catlin added: “We would strongly urge that anyone with any information comes forward and assists with the ongoing police enquiries.
“The vast majority of fans were a credit to their respective clubs, but the actions of a small minority last Saturday is not how PFC expect supporters to behave and we now await to hear what sanctions The FA and EFL could place on the club.”
Anyone with information is asked to contact police on 101, quoting 44170356118, or call the charity Crimestoppers anonymously on 0800 555 111.